Numerical Solution of Bending Problem for Elliptical Plate Using Differentiation Matrix Method Based on Barycentric Lagrange Interpolation

Abstract

A differentiation matrix method based on barycentric Lagrange interpolation for numerical analysis of bending problem for elliptical plate is presented. Embedded the elliptical domain into a rectangular, the barycentric Lagrange interpolation in tensor form is used to approximate unknown function. The governing equation of bending plate is discretized by the differentiation matrix derived from barycentric Lagrange interpolation to form a system of algebraic equations. The boundary conditions on curved boundary are directly discretized using barycentric Lagrange interpolation. Combining discrete algebraic equations of governing equation and boundary conditions to form an over-constraints system of equations, the numerical solutions on rectangular can be obtained by solving it. Then, the numerical solutions on elliptical domain are obtained by interpolating the data on rectangular. Numerical results of elliptical plate with uniform load illustrate the effectiveness and accuracy of the proposed method.